Recent content by gabee

Got it. That's a great explanation, thank you very much!

Can someone help clarify this equation from classical dynamics? It doesn't seem to make sense. Here's my textbook's explanation. A particle has position vector \vec{r} in a non-rotating, inertial reference frame (the 'un-prime' frame). Suppose we want to observe the motion of this object in...

This is right. No, rest is the state in which the velocity of an object is 0 with respect to the reference frame...as you showed, the object is at rest momentarily when \omega t = \frac{\pi}{2} (with respect to the frame of the coordinate system). It doesn't necessarily mean that all...

If you envision the transmission line as a big resistor, you have a circuit that looks like an AC power supply connected to that big resistor. You could send the same amount of power through the line by having either low voltage/high current or high voltage/low current, or somewhere in between...

A correction here: current isn't depleted after passing through a resistor or a light bulb. The same current enters the resistor as that which exits (by Kirchoff's laws). It is the voltage that is "diminished"; i.e. there is a potential drop from one side of the resistor to the other.

Here is an analogous case with a mass on a spring, you should be able to spot the error. If you have a mass on a spring, and you displace it and let it go, it will freely oscillate. But, at a certain time, it passes through the equilibrium position. When it is at the equilibrium position, there...

It is written by a mathematician and so a lot of the examples are from a mathematical standpoint, but the author clearly emphasizes that the very general principles he details in the book could be used equally well for someone trying to solve a problem in mathematics, physics, economics...

I am reading a book that has pretty good reviews, called "How to Solve It" by G. Polya. It focuses on how to go about solving problems. I would really recommend it, it will probably help you think more clearly about finding a "path" to solve a given problem. You also need to have confidence in...

Hmm. Using the equation dp = dm*V must implicitly assume that V is constant wrt the variable by which you differentiate. If that variable is length x, say, then m=m(x) and V=V(x). Then \frac{dp}{dx} = V\frac{dm}{dx} + m\frac{dV}{dx}. First, it's important to note immediately that this is...

If the angle is one of the most commonly used ones (i.e. the ones listed on the unit circle), you can do this. Enter sin(pi/3)...the calculator will tell you it is 0.866025404. Since you know that the common sine/cosine values are things that have a square root in the numerator, you might want...

Hm, let me try to explain... You can tell that the expression on the left is essentially just the limit definition of the derivative that you learned in Calc 1, except for the fact that now it's a function that takes a vector that we're taking the derivative of. The derivative is being...

E8. Get ready for pain.

Geometry was one of the major early developments in the study of mathematics. Today our technical problems have advanced beyond the point where we can just apply simple geometrical principles, but the study of geometric principles at the high school level is still extremely important. I like to...

1. Google says Bhutan. 2. Google doesn't know. :/ 3. Google says Thailand. 4. Google says Us. 5. Wikipedia says Algiers (Algeria) and Djibouti (Djibouti).

What's strange (and slightly worrisome) is that a google query for the edge movie needle silk compass yields several sites telling users that silk magnetization really works...